[Show abstract][Hide abstract] ABSTRACT: It is well-known that there exist no homogeneous ruled real hypersurfaces in a complex projective space. On the contrary there exists the unique homogeneous ruled real hypersurface in a complex hyperbolic space. Moreover, it is minimal. We characterize geometrically this minimal homogeneous real hypersurface by properties of extrinsic shapes of some curves.
Journal of the Mathematical Society of Japan 01/2009; 61(2009). DOI:10.2969/jmsj/06110315 · 0.62 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We characterize real hypersurfaces of type (A) and ruled real hypersurfaces in a complex projective space in terms of two φ-invariances of their shape operators, and give geometric meanings of these real hypersurfaces by observing their some geodesics.
[Show abstract][Hide abstract] ABSTRACT: In this paper, we classify the real hypersurfaces in a non-flat complex space form with η-parallel shape operator.
KeywordsComplex space forms–Hopf hypersurfaces–Ruled real hypersurfaces–
η-parallel shape operator
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